Ciudadanos on Tuesday put forward six conditions - including electoral reform and anti-corruption measures - which if accepted would see it sit down to negotiate with the PP and back the ruling conservative party in its bid to form a minority government.
This would be the first breakthrough after inconclusive elections in June, although Rajoy would still need support elsewhere to break Spain's deep-set political paralysis and get a government through the necessary parliamentary vote of confidence.
The PP "will do everything in its power to allow these negotiations to start", Rajoy told reporters after meeting with Ciudadanos chief Albert Rivera, adding the party's executive committee would meet next Wednesday to examine and vote on the proposals.
Spain has been without a fully functioning government for more than seven months following two inconclusive polls, leaving it in political limbo in a sensitive economic and political period.
But even as parties reiterate the need for a stable government after repeat elections in June, none has yet sealed a deal, leaving the country in the hands of a caretaker government.
Rajoy's PP, in power since 2011, won the June elections but fell short of an absolute majority, winning 137 parliamentary seats out of 350.
The acting prime minister has since been tasked by King Felipe VI with forming a coalition or minority government, which he will have to push through a vote of confidence.
In order to do so, Rajoy will need an absolute majority in the vote. If he fails, a second vote will be held several days later in which he would only need a simple majority.
But Ciudadanos, with the 32 seats it gained in June elections, will still not be enough for Rajoy to push a government through if everyone else votes against it.
He still needs the help of the Socialists, even if it is just an abstention in the vote.
But they have so far ruled out abstaining.